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arXiv · 1411.4861

A note on reduced and von Neumann algebraic free wreath products

Jonas Wahl
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Abstract

In this paper, we study operator algebraic properties of the reduced and von Neumann algebraic versions of the free wreath products $\mathbb G \wr_* S_N^+$, where $\mathbb G$ is a compact matrix quantum group. Based on recent result on their corepresentation theory by Lemeux and Tarrago, we prove that $\mathbb G \wr_* S_N^+$ is of Kac type whenever $\mathbb G$ is, and that the reduced version of $\mathbb G \wr_* S_N^+$ is simple with unique trace state whenever $N \geq 8$. Moreover, we prove that the reduced von Neumann algebra of $\mathbb G \wr_* S_N^+$ does not have property $\Gamma$.

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Jonas Wahl. 2014-11-18. A note on reduced and von Neumann algebraic free wreath products. https://arxiv.org/abs/1411.4861

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